A190970 a(n) = 5*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.

0, 1, 5, 16, 35, 31, -160, -1079, -3955, -10064, -14725, 16951, 217280, 933841, 2713685, 5163856, 1396115, -39494129, -210035680, -694731239, -1583335075, -1664094224, 5929544555, 44624570791, 169756952960, 447163627681, 708005561765, -484444840304

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-9).

Formula

G.f.: x/(1 - 5*x + 9*x^2). - Philippe Deléham, Oct 12 2011

a(n) = 3^(n-1) * ChebyshevU(n-1, 5/6). - G. C. Greubel, Jun 09 2022

From Peter Bala, Sep 22 2025: (Start)

a(n) = 1/sqrt(-11) * ( (5 + sqrt(-11))^n - (5 - sqrt(-11))^n )/2^n.

E.g.f.: (2/sqrt(11)) * exp(5*x/2) * sin(sqrt(11)*x/2).

Sum_{n >= 1} a(n)*x^(2*n)/(2*n)! = (2/sqrt(11)) * sinh(sqrt(11)*x/2) * sin(x/2). (End)

Maple

A190970 := proc(n)
    option remember ;
    if n <= 1 then
        n;
    else
        5*procname(n-1)-9*procname(n-2) ;
    end if;
end proc: # R. J. Mathar, Mar 23 2023

Mathematica

LinearRecurrence[{5, -9}, {0, 1}, 50]

Prog

(Magma) [n le 2 select n-1 else 5*Self(n-1) - 9*Self(n-2): n in [1..51]]; // G. C. Greubel, Jun 09 2022
(SageMath) [3^(n-1)*chebyshev_U(n-1, 5/6) for n in (0..50)] # G. C. Greubel, Jun 09 2022

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A096941 A246697 A098404 * A077415 A234362 A363613

Adjacent sequences: A190967 A190968 A190969 * A190971 A190972 A190973

Keyword

sign,easy

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Status

approved